A remark on the problem of nonnegative k-subset sums

A remark on the problem of nonnegative k-subset sums Given a set of n real numbers with a nonnegative sum, consider the family of all its k-element subsets with nonnegative sums. How small can the size of this family be? We show that this problem is closely related to a problem raised by Ahlswede and Khachatrian in [1]. The latter, in a special case, is nothing else but the problem of determining a minimal number c n (k) such that any k-uniform hypergraph on n vertices having c n (k) + 1 edges has a perfect fractional matching. We show that results obtained in [1] can be applied for the former problem. Moreover, we conjecture that these problems have in general the same solution. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Problems of Information Transmission Springer Journals

A remark on the problem of nonnegative k-subset sums

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Publisher
SP MAIK Nauka/Interperiodica
Copyright
Copyright © 2012 by Pleiades Publishing, Ltd.
Subject
Engineering; Communications Engineering, Networks; Electrical Engineering; Information Storage and Retrieval; Systems Theory, Control
ISSN
0032-9460
eISSN
1608-3253
D.O.I.
10.1134/S0032946012040059
Publisher site
See Article on Publisher Site

Abstract

Given a set of n real numbers with a nonnegative sum, consider the family of all its k-element subsets with nonnegative sums. How small can the size of this family be? We show that this problem is closely related to a problem raised by Ahlswede and Khachatrian in [1]. The latter, in a special case, is nothing else but the problem of determining a minimal number c n (k) such that any k-uniform hypergraph on n vertices having c n (k) + 1 edges has a perfect fractional matching. We show that results obtained in [1] can be applied for the former problem. Moreover, we conjecture that these problems have in general the same solution.

Journal

Problems of Information TransmissionSpringer Journals

Published: Jan 24, 2013

References

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